Problem: Solve for $x$, ignoring any extraneous solutions: $\dfrac{x^2}{x - 7} = \dfrac{49}{x - 7}$
Solution: Multiply both sides by $x - 7$ $ \dfrac{x^2}{x - 7} (x - 7) = \dfrac{49}{x - 7} (x - 7)$ $ x^2 = 49$ Subtract $49$ from both sides: $ x^2 - (49) = 49 - (49)$ $ x^2 - 49 = 0$ Factor the expression: $ (x + 7)(x - 7) = 0$ Therefore $x = -7$ or $x = 7$ However, the original expression is undefined when $x = 7$. Therefore, the only solution is $x = -7$.